Ejercicios

# Calculo 1: P(X >= 4.5)
p1 <- pnorm(4.5, mean = 0, sd = 1, lower.tail = FALSE)
cat("P(X >= 4.5) =", p1, "\n")

## P(X >= 4.5) = 3.397673e-06

# Calculo 2: Encontrar k tal que P(X <= k) = 0.1056
k1 <- qnorm(0.1056, mean = 0, sd = 1)
cat("k tal que P(X <= k) = 0.1056 es:", k1, "\n")

## k tal que P(X <= k) = 0.1056 es: -1.250273

# Calculo 3: Encontrar k tal que P(Z >= k) = 0.4801
k2 <- qnorm(1 - 0.4801, mean = 0, sd = 1)
cat("k tal que P(Z >= k) = 0.4801 es:", k2, "\n")

## k tal que P(Z >= k) = 0.4801 es: 0.04990261

# Calculo 4: Hallar k tal que P(X > k) = 0.05
k <- qnorm(0.95, mean = 0, sd = 1)
cat("k tal que P(X > k) = 0.05 es:", k, "\n")

## k tal que P(X > k) = 0.05 es: 1.644854